Determination of Crystal Structure of Graphitic Carbon Nitride: Ab Initio

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Determination of Crystal Structure of Graphitic Carbon Nitride: Ab Initio Evolutionary Search and Experimental Validation Junjie Wang,*,†,‡ Dong Hao,† Jinhua Ye,† and Naoto Umezawa*,†,§ †

International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan ‡ Materials Research Center for Element Strategy, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8503, Japan § Center for Materials research by Information Integration (CMI2), National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan S Supporting Information *

ABSTRACT: Although graphitic carbon nitride (g-C3N4) is a promising photofunctional material, its structure is poorly understood. Here, we present a systematic study of stable crystal structures of g-C3N4 by ab initio evolutionary searching. It was discovered that off-plane distortion of heptazine units is a characteristic of the most stable structure, which explains a known discrepancy between the lattice parameters determined by X-ray diffraction (XRD) patterns and the planar structures modeled in previous studies. A phase transition from a metastable phase to the global minimum phase provides a reasonable explanation for the observed red shift in photoabsorption edges upon high-temperature annealing. The recently suggested salt-melt synthesis for g-C3N4 is subject to the contamination of hydrogen, chlorine, and lithium according to our detailed analysis of the crystal structures of C6N9H3-Li3Cl and C6N9H3-LiCl in comparison with the measured XRD patterns of these samples. Finally, a viable synthesis pathway for purifying high-crystallinity g-C3N4 is proposed.

1. INTRODUCTION Graphitic carbon nitride (g-C3N4), which is believed to possess a graphitelike layered structure, has attracted extensive interest because of its promise as a metal-free photocatalyst1−9 and its potential applications in optoelectronics.10−14 However, the basic characteristics of g-C3N4 (e.g., electronic and optical properties) are not well understood because the ground-state crystal structure of g-C3N4 is still unclear. Clarification of the structure of g-C3N4 is, therefore, a challenge and crucial for understanding its properties, both experimentally and theoretically. Much effort15−26 has already been applied to identify the structures of g-C3N4. Normally, the g-C3N4 samples used in research are synthesized by thermal polycondensation in air (Figure 1a). When using this method, however, the greatest obstacle to experimentally confirming the crystal structure of gC3N4 is that a sample with high crystallinity cannot be obtained. The information that can be obtained through crystallographic methods has been insufficient and limited to two slightly temperature-dependent X-ray diffraction (XRD) peaks at 2θ = 13.04° and 27.25°. Researchers believe that these two peaks correspond to an in-plane ordering with a repeated distance of about 6.788 Å and a planar graphitic interlayer distance of about 3.273 Å, respectively. Two kinds of elementary building blocks, triazine and heptazine (tris-s-triazine), have been © 2017 American Chemical Society

assumed to construct an ideal model structure of g-C3N4. The heptazine ring is energetically more favored according to a computational stud,y2,19 and its dimension of about 7.13 Å is close to the value of the coplanar repetition distance of 6.788 Å assigned for the peak at 2θ = 13.04° in the XRD pattern. Hence, many researchers have suggested that heptazine rings linked by trigonal nitrogen atoms constitute the most stable local connection pattern (see the structure illustrated in Figure 1a). Recent studies20,22 have also suggested that carbon nitride is composed of graphitelike A−B stacks. However, the exact stacking positions of the atoms with respect to the adjacent layers are still unclear because of the experimental limitations, and further study is needed to clarify the stacking order as well as the local geometry. Recently, salt-melt synthesis (SMS) of g-C3N4, first proposed by Bojdys et al.,19 has emerged as an important alternative to conventional thermal polycondensation. By employing this method, we obtained a uniform crystalline sample, as shown by the fine peaks in the XRD pattern in Figure 1b. However, the crystal model proposed by Bojdys et al. does not match the diffraction patterns, possibly because it was fitted under the Received: July 20, 2016 Revised: March 12, 2017 Published: March 13, 2017 2694

DOI: 10.1021/acs.chemmater.6b02969 Chem. Mater. 2017, 29, 2694−2707

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Chemistry of Materials

Figure 1. Synthesis of g-C3N4 by thermal polycondensation and SMS using the same precursor dicyandiamide (DCDA, C2H4N4). (a) XRD pattern and suggested crystal structure of g-C3N4 synthesized by thermal polycondensation. In the thermal polycondensation process, DCDA was placed in an alumina crucible with a lid and heated to 550 °C in an air atmosphere for 4 h. (b) XRD pattern of g-C3N4 synthesized by SMS. In the SMS process, DCDA was thoroughly ground together with a mixture of LiCl and KCl and heated under an inert atmosphere at 400 °C for 6 h and then sealed in a quartz glass ampule followed by heating at 580 °C for 6 h. In this and following figures, the blue and light gray balls represent N and C atoms, respectively.

searching.27−29 Starting from our experimental data of thermal condensation, we revealed the most stable configuration of heptazine-based g-C3N4 for the first time by ab initio evolutionary searching. Our computational investigation corresponding to SMS confirms that the highly crystalline SMS sample we obtained was not g-C3N4 but C6N9H3·LixCl (1 ≤ x ≤ 3). Finally, a possible reaction pathway from C6N9H3· LixCl (1 ≤ x ≤ 3) to g-C3N4 is proposed based on our computational analysis.

assumption that the sample was free from any potential impurities such as hydrogen, chlorine, or lithium, which are the constituent elements of the precursors for the SMS synthesis of g-C3N4. Schnick and co-workers24 suggested a lamellar structure with intercalated LiCl based on thorough nuclear magnetron resonance spectroscopy and diffraction studies, although their results did not reproduce the XRD result. Bojdys and co-workers25 reported that triazine-based g-C3N4 could be detected at the gas−liquid and solid−liquid interfaces in the reactor of SMS, which suggests that the SMS condition can promote the production of g-C3N4 with triazine units. However, the crystal structure of detected g-C3N4 could not be determined because of a lack of observable XRD peaks for bulk g-C3N4. Hence, further studies on the effects of impurities on the SMS sample are required to precisely determine its crystal structure. Figure 1 shows that the procedures for the syntheses of gC3N4 by thermal polycondensation and SMS involve air and inert atmospheres, respectively. Previous experimental investigations showed that the conditions of synthesis have a significant effect on the final structure of g-C3N4,1,2,19,25 although a clear explanation for the effect was not provided. In the present work, to answer this question, we first studied the synthesis reaction pathway proceeding through intermediates to g-C3N4 from dicyandiamide (DCDA, C2H4N4) in air and inert atmospheres by using density functional theory (DFT) calculations. Then, we carried out a global search for stable structures of g-C3N4 and intermediates corresponding to different atmospheres using ab initio evolutionary structure

2. COMPUTATIONAL AND EXPERIMENTAL DETAILS 2.1. Structure Prediction using ab initio Evolutionary Algorithm. Our computational structure searches were performed using Universal Structure Predictor: Evolutionary Xtallography (USPEX)27−29 and VASP codes.30,31 A detailed introduction to structure searching and a typical USPEX input file for the structure search of g-C3N4 can be found in the Supporting Information. We performed first-principles calculations using the generalized gradient approximation in the Perdew−Burke−Ernzerhof (PBE)32 form as implemented in VASP. The projector-augmented wave method was employed to treat core electrons, while the N (2s22p3) and C (2s22p2) electrons were treated as valence electrons. As we know, a nonlocal van der Waals (vdW) bonding exists between the carbon nitride layers and cannot be properly described by standard DFT. In recent works,33−35 the influence of vdW interaction on the structural parameters and the electronic properties of layered structures has been highlighted. A strong vdW interaction between the g-C3N4 layers is definitely expected. In the structure search, to correctly describe the nonbonded dispersion forces between g-C3N4 layers, we included the van der Waals correction by using the method of Tkatchenko and 2695


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Chemistry of Materials Scheffler with self-consistent screening (it is referred to as PBE+TSSCS in this paper).36−40 The plane-wave kinetic-energy cutoff was 550 eV, and the Γ-centered k-point mesh resolution was 2π × 0.06 Å−1. 2.2. Structure Optimization and Electronic Structure Calculation. For the optimization of the most stable structures and the subsequent band structure calculations, we improved the cutoff energy and k-point sets to 900 eV and 2π × 0.04 Å−1, respectively. The convergence criterion for the geometry optimization was set to require the force on the atoms to be less than 0.001 eV/Å. Recent studies33,40 revealed that the vdW-corrected screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE)41,42 can be a good choice to extend layered structures to obtain good descriptions of both nonbonded dispersion and electronic structure. We had carried out a detailed test by using different functionals (details of the functional test are presented in Supporting Information and shown in Figure S1). After considering all the optimized lattice parameters of g-C3N4, a, c, and c/ a, we concluded that HSE06-TS-SCS, which was developed by Tkatchenko and Scheffler,36−40 gives the best overall estimation. Therefore, the lattice constants and atomic coordinates obtained with HSE06-TS-SCS were used for the calculations of electronic properties in the present work, which were also performed within the vdW correction framework of HSE06-TS-SCS. The chemical bonds in heptazine-based g-C3N4 were analyzed by conducting crystal orbital overlap populations (COOP) analysis, using the LOBSTER code43−46 and density of states (DOS) calculations based on VASP outputs. These calculations were performed using the same settings as the band structure calculations with the exception of a denser k-mesh (Monkhorst−Pack mesh solution of 2π × 0.02 Å−1) for DOS and COOP analysis. 2.3. Phase Transition Calculation. To study the phase transition of g-C3N4 in the present work, we performed the transition state searches using a synchronous transit method47 implemented in the CASTEP code.48 We performed complete linear synchronous transit (LST)/ quadratic synchronous transit (QST) calculations by starting with a calculation to optimize LST (see detailed introduction in the Supporting Information). 2.4. Synthesis of g-C3N4, C6N9H3-Li3Cl, and C6N9H3-LiCl. The traditional g-C3N 4 was synthesized in static air by thermal polycondensation of dicyandiamide (DCDA; >98.0%) according to the procedure reported in a previous study.1 In a typical process, 2 g of DCDA was placed in a lidded alumina crucible, which was inserted into a muffle furnace and heated to 550 °C at a ramp rate of 2.3 °C/ min for 4 h. After cooling to 25 °C, the resultant yellow product was ground into powder in an agate mortar. The eutectic SMS method proposed in the literature19 was adopted to synthesize the highcrystallinity sample of C6N9H3-Li3Cl and was modified for the synthesis of C6N9H3-LiCl. The details are described in Supporting Information. 2.5. Materials Characterization. X-ray diffraction patterns were recorded on an X-ray diffractometer with Cu Kα X-ray radiation (λ = 0.15418 nm) in a scanning angle (2θ) range of 5°−60° (X’pert PRO; PANalytical Co., The Netherlands). The diffuse reflection spectra were measured with an integrating-sphere-equipped UV−visible recording spectrophotometer (UV-2600, Shimadzu Co., Japan) using BaSO4 as the reference, and the optical absorptions were converted from the respective reflectance spectra according to the Kubelka−Munk equation. The simulated XRD patterns of the predicted structures in the present work were obtained using analytical and crystallization software (Materials Studio Reflex Powder Diffraction, BIOVIA). The experimental XRD settings were adopted in the simulation to ensure the validity of the comparison.

Figure 2. Synthesis of g-C3N4 by thermal polycondensation and SMS using the same precursor dicyandiamide (DCDA, C2H4N4) and its possible reaction mechanism. (a) Pathways for the first three steps of the condensation of DCDA. (b) Free energy profile in inert environment. (c) Free energy profile in an air environment. Both of the profiles were obtained using the Helmholtz free energy and were computed at 800 K, which is a typical temperature for the synthesis of g-C3N4.

through melem to form heptazine-based g-C3N4 or directly transferring to triazine-based g-C3N4. It appears that different structures of g-C3N4 can be obtained by carefully controlling the condensation conditions. Therefore, to reveal the underlying mechanism, we calculated the overall Helmholtz free energy profiles from DCDA to melem corresponding to different synthesis atmospheres. The details of the free energy computation are presented in the Supporting Information. Figure 2b shows the free-energy profile of DCDA condensation in an inert atmosphere, which corresponds to the following reactions: 3C2N4H4 → 2C3N6H6 → C6N11H 9 + NH3 → C6N10H6 + 2NH3

(1)

The figure indicates that the first step of melamine formation by the molecular reaction of DCDA is a downhill exothermic reaction with an energy release of 3.75 eV. However, the successive deamination processes are endothermic. As illustrated in Figure 1b, the first step of the SMS of DCDA is to heat the mixture of DCDA and LiCl/KCl in an open inert environment (Ar flux) at 400 °C. As demonstrated in the previous experiment,19 this temperature is too low to promote the full condensation of DCDA, although the Ar flux will also help the deamination by transporting the produced ammonia away from the sample. The situation is not improved much by the successive annealing at 600 °C under a vacuum in a sealed quartz tube. Therefore, it is expected that the deamination reaction shown in Figure 2a can only proceed to an incomplete degree. In fact, there should be a good chance of trapping the final product during the formation of melam, which still has a rather high concentration of ammonia. In the normal thermal polycondensation of DCDA (Figure 1a), the involvement of O2 from the surrounding air is unavoidable. Hence, we incorporated the following reaction to

3. RESULTS AND DISCUSSION 3.1. Pathway of the Condensation of DCDA. As proposed in the literature,19 Figure 2a illustrates the pathway of thermal condensation of the DCDA starting material toward g-C3N4. It shows that this condensation is driven by deamination and the formation of aromatic units. We can see that melam can further branch into two channels: advancing 2696


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Chemistry of Materials calculate the free energy profile of DCDA polycondensation in air: 3C2N4H4 + 1.5O2 → 2C3N6H6 + 1.5O2 → C6N11H 9 + 0.75O2 + 1.5H 2O + 0.5N2 → C6N10H6 + 3H 2O + N2

(2)

After the introduction of O2, the deamination steps shown in Figure 2c are thermodynamically favored, with a dramatic energy decrease accompanying each step. Figure 2a illustrates that the deamination process will lead to the production of melem, a direct precursor of heptazine-based g-C 3N 4. Consequently, our free energy calculations suggest that the production of heptazine-based g-C3N4 is highly energetically favored in an air atmosphere, which is consistent with the results of previous experiments. The free energy profile calculations offer important clues to why the structures synthesized in thermal polycondensation and SMS are so different. Therefore, we performed an evolutionary structure search based on two assumptions: (1) the air atmosphere in the thermal polycondensation process favors the production of heptazine-based g-C3N4. It is worth mentioning that defects have been reported in g-C3 N4 synthesized by thermal polycondensation.49 However, defects were not considered in the present study because based on the calculated free energy profile (Figure 2c), we believe C3N4 will be the dominant phase in the product. The effect of defects on the properties of g-C3N4 is certainly important and must be studied in future investigations. (2) The high-crystallinity sample obtained by SMS contains a rather high concentration of extra ammonia. Lithium and chlorine can also be included owing to the use of LiCl in the SMS synthesis. 3.2. Model Structures of g-C3N4 Optimized under Assumption 1. 3.2.1. Ab Initio Evolutionary Structure Search. The following clues to the g-C3N4 structure obtained from thermal polycondensation1,2,18 were gathered from the evolutionary structure search: an in-plane repetition distance of 6.788 Å, which is comparable with the size of a heptazine unit (about 7.13 Å) and an interlayer distance of about 3.273 Å. Therefore, it is reasonable to assume that there are two layers of C3N4 in a primitive lattice and that each layer consists of one heptazine unit, which is composed of six carbon and eight nitrogen atoms. The search was performed with 28 atoms per unit cell. More than 4000 structures were sampled in this search to confirm the reliability of the final result. The most stable structures, phases 1−3, are shown in Figure 3. The pathway in Figure 2a shows that melem can be regarded as the direct precursor for the heptazine-based g-C3N4. To confirm the thermal stability of g-C3N4, we calculated the Helmholtz free energy change from melem to the most stable g-C3N4 (phase 1) in air using the following equation: C6N10H6 + 1.5O2 → 2C3N4 + 3H 2O + N2

Figure 3. Prediction of heptazine-based g-C3N4. (a) Predicted most stable configuration, phase 1; (b) second stable distorted configuration, phase 2; (c) most stable planar configuration, phase 3. The atoms in the middle layer of the lattices are labeled with yellow crosses.

Figure 4. (a) Detailed structure of a distorted heptazine unit and (b) possible rearrangement route from phase 2 to phase 1. The red arrows indicate the directions of movement of the atoms.

(3)

through the atoms Nlink, Ncen, and C1. The significant difference between g-C3N4 and the typical honeycomb layered structures (e.g., graphite and h-BN) is that each layer consists of heptazine units and pores. Therefore, g-C3N4 is more susceptible to distortion. Our calculation shows that the distortion will considerably stabilize the structure. The computed phonon dispersion of phase 1 shows no imaginary frequency (Figure S2a), thus confirming the dynamic stability of the thermodynamically stable phase. The relative energy difference and lattice parameters of three predicted g-C3N4 structures and two planar structures reported

The calculated energy change of −17.20 eV per formula unit shows that the condensation of heptazine-based g-C3N4 is thermodynamically favored. All the predicted structures exhibit graphitelike sheets that consist of polymerized heptazine units and pores with comparable sizes, and they are aligned with the A−B stacking configuration. Interestingly, the N and the C atoms in phases 1 and 2 were found to be distorted from those in the planar-layered structure represented by phase 3. Figure 4a shows that the peripheral nitrogen atoms, Nper, and the carbon atoms C2 and C3 are shifted around an axis passing 2697


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Table 1. Comparison of Energetics, Lattice Parameters, and Band Gap of Predicted g-C3N4 Structures with Those Reported in the Literature18 (T1 and T2)a Eg (eV)

lattice constant (Å) structure

ΔE(eV)/C3N4

symmetry

a

c

c/a

volume (Å3)

direct

indirect

phase 1 phase 2 phase 3 T1 T2 experiment

0 0.056 0.313 0.329 0.532 −

C2221 Aba2 Amm2 P̅6m2 P̅6m2 −

6.898(1.62) 6.893(1.55) 7.061(4.01) 7.060(4.00) 7.060(4.00) 6.788

6.679(2.03) 6.754(3.18) 6.414(−2.02) 6.536(−0.15) 7.141(9.09) 6.546

0.968 0.980 0.908 0.926 1.011 0.964

275.800 278.377 276.873 282.130 308.265 261.86

2.87 3.17 2.66 2.64 2.43 2.86

− 3.14 2.27 2.27 2.17 −

a

Detailed information on the crystal structure of the predicted structures can be found in the Crystallographic Information Files of Predicted Structures.

by Tyborski et al.18 (hereafter referred to as T1 and T2) are listed in Table 1; the experimental data are also listed for comparison. The vertical lattice constant, c, which is twice the interlayer distance, shows a dependence on the stacking modes. For example, the values of c are 6.414, 6.536, and 7.141 Å for the planar configurations of phase 3, T1, and T2, respectively. The A−A stacking structure of T2 exhibits a much larger value of c than those of the A−B stacking structures of phase 3 and T1. On the other hand, the lateral lattice constant a is influenced by the distortion. In the earlier studies,1 researchers gave an ambiguous explanation that the possible tilt angularity of g-C3N4 could be the reason that the lateral lattice constant (∼ 6.81 Å) is smaller than the size of heptazine units (∼ 7.13 Å). Our predicted crystal structures explicitly reveal that this difference originates from the distortion of the basic g-C3N4 unit. Here, we propose the concept of “micro” and “macro” A−B stacking sequences. We name the stacking sequence of −C− N−C−N− along the c direction observed in phases 2 and 3 as “micro” A−B stacking, where there is only a shift of C and N atoms with respect to those in the adjacent layers, without rotation of the heptazine units. However, phase 1, the most stable configuration of g-C3N4, exhibits a unique structure in which the heptazine units in one layer are rotated by 60° with respect to the basic units in the adjacent layers. If we regard the heptazine units and the pore regions as “macro” A and B sites, respectively (Figure 3a), phase 1 exhibits a perfect “macro” A− B stacking arrangement in which the heptazine units sit exactly on the pores of the adjacent layer. The lowest energy of phase 1 reveals that the “macro” A−B stacking manner can stabilize the g-C3N4 structure to the greatest extent. Moreover, neither bare PBE nor HSE06 calculations yields significant differences in the total energy of phase 1 and the metastable phases, and the lattice parameter c of phase 1 is largely overestimated when the vdW interaction is omitted (Figure S1). These results prove that vdW interaction plays an important role in stabilizing the layered structures of g-C3N4. 3.2.2. Phase Transition. It was observed in previous experiments1−4 that the optical absorption edge of g-C3N4 is shifted toward the longer-wavelength region with increasing condensation temperature, indicating a slight dependence of the band gap on the reaction temperature. To study the effect of annealing temperature on the variation in band gap of gC3N4, a possible phase transition between different phases of gC3N4 was investigated, and the results are discussed in this section. It is reasonable to assume that the g-C3N4 obtained in the experiments was a mixture of the different phases, such as phase 1 and phase 2, which possess different band gaps, as discussed in the following section. The computed Gibbs free

energy (Figure S3(a)) shows that phase 1 possesses lower free energy than phase 2. Therefore, there is a thermodynamic purpose for the transition from phase 2 to pPhase 1. Thermodynamically, the rate at which a system overcomes the energy barrier for the transition from a metastable phase to the most stable phase is increased as the temperature is raised. Hence, the higher the reaction temperature, the greater the probability for the phase transition from phase 2 (with a wider direct band gap, 3.17 eV) to phase 1 (with a smaller direct band gap, 2.87 eV). Consequently, the reaction-temperature dependence of the band gap of g-C3N4 can be observed. Our structural studies of phases 1 and 2 showed that the three Nlink−C bonds located at the corner of a heptazine unit (Figure 4a) are about 11% longer than other N−C bonds (Table S1). Among the three Nlink−C bonds, two (Nlink−C2) are identical to each other and are 1% longer than the third one (Nlink−C4). On the basis of this observation, a possible rearrangement route from phase 2 to phase 1 was proposed (as illustrated in Figure 4b): first, the two longer Nlink−C bonds break; next, a 60° rotation of a heptazine unit occurs; and finally, the lattice and the atomic positions relax to the configuration of phase 1. To support our hypothesis, a search for a transition state between phase 2 and phase 1 was carried out based on the route illustrated in Figure 4b. A reaction pathway between the initial and the final configurations was interpolated using the synchronous transit method.47,48 Finally, we found a transition state with an energy barrier of 1.87 eV/C3N4 referenced to phase 2 (Figure S4a). After the introduction of entropy contributions of phase 1, phase 2, and the transition state (Figure S4b), the energy barriers of the phase transition were updated, as shown in Figure S4(c). Following the classical absolute rate theory,50−52 the jump rate to overcome the energy barrier in the experimental temperature range can be estimated by the equation ⎛ E ⎞ Γ = Γ0 exp⎜ − b ⎟ , ⎝ kBT ⎠

(4)

where Γ is the jump rate of the phase transition from the initial to the final structure, Γ0 is the ratio of the vibrational frequencies of the initial configuration to the frequencies of the transition state structure, kB is the Boltzmann constant, T is the temperature, and Eb is the energy barrier shown in Figure S4(c). The most important feature of eq 4 is that an increase of a few degrees in the temperature results in a sizable increase in the jump rate by several orders of magnitude. This indicates that the jump rate is dominated by the energy barrier Eb rather than Γ0, and thus it is common to use a typical value51−53 of 2698


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Figure 5. Electronic structures of the predicted phases 1 and 3. Calculated band structures of (a) phase 1 and (b) phase 3; calculated partial charge densities of π1, π1*, and LP states at the VBM and CBM of (c) phase 1 and (d) phase 3.

atomic vibration frequency between 1012 and 1013 s−1 for Γ0. A value of 5 × 1012 was adopted for Γ0 in our estimation. The jump rates of the phase transition between phase 1 and Pphase 2 were estimated in the typical temperature range for the synthesis of g-C3N4 (i.e., between 673 and 883 K),1−3 and the results are shown in Figure S4d. They show that a jump rate Γ ≥ 1 s−1 (indicating that the transition takes place with a high possibility) for the phase transition from phase 2 to phase 1 can be obtained when the temperature is higher than 770 K. In the same temperature range, the jump rate for the reverse transition from phase 1 to phase 2 is much lower than that for the transition from phase 2 to phase 1. Therefore, the transition from the meta-stable state (phase 2) to the ground state (phase 1) is the dominant reaction process at the elevated temperature if we assume that phase 1 and phase 2 coexist in the as-prepared samples. As the temperature increases, so does the fraction of the material that has undergone the phase transition. Therefore, phase 1 with a smaller band gap would predominate. This explains the main features of the reaction-temperature dependence of the band gap of g-C3N4. 3.2.3. Electronic Properties of Predicted g-C3N4. We performed electronic structure calculations for phases 1−3, and their band gaps are presented in Table 1. Our computational results for the previously suggested planarshaped T1 and T2 phases are also listed in Table 1. It is understood that phase 1 possesses a direct band gap of 2.87 eV

(Figure 5a), whereas phases 2 and 3 possess indirect band gaps of 3.14 eV (Figure S5) and 2.27 eV (Figure 5b), respectively. Meanwhile, the band gaps of T1 (2.27 eV) and T2 (2.17 eV) are much narrower than the experimental value. The computed band gap of phase 1 is consistent with the experimental band gap of g-C3N4 synthesized by thermal condensation. Surprisingly, the interlayer distance (listed in Table 1) does not influence the band gap, which is contrary to the trend exhibited by other layered materials.33,54 Instead, the distortion of the heptazine unit was found to determine the band gap, and the distortion of the heptazine unit is strongest in phase 2 (Table S2). Consequently, phase 2 has the widest band gap, as shown in Table 1. In a planar structure like that in phase 3, the valence band maximum (VBM) consists of antibonding states of lone pair (LP) electrons of peripheral nitrogen, while pz orbitals on these nitrogen sites form π1 bands right below the LP band [Figure 5 (panels b and d) and Figure S6 (panel c and d)]. It is understood that the repulsion between the LP orbitals in phase 3 is strong because lobes of the LP orbitals at different Nper sites lie on the same heptazine plane, and electrons occupying these orbitals are closely distributed (Figure 5d). As a result, the LP band is higher than the π1 band in phase 3 (Figure 5b). The electronic structure at the VBM is drastically changed by the distortion of the heptazine unit, as observed in the band structures for phase 1 and phase 2 (Figure 5a). The LP bands are largely shifted downward and partially hybridized 2699


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Chemistry of Materials with the π1 bands. This originates from the release of the LP orbitals toward the off-plain open space; the lobes protrude from the heptazine plane (Figure 5c), alleviating the Coulombic repulsive interactions among the LP orbitals. The distortion, therefore, greatly stabilizes the system, giving a clear explanation of why phase 1 and phase 2 are energetically favored over phase 3. We also observed that the Nper−Nper distances across the peripheral nitrogen atoms are slightly increased in phase 1 and phase 2 (Table S2). The on-site LP−π1 hybridization, which also contributes to the stabilization of the system, is manifested as resonance of the two orbitals in the band structure (Figure 5a) and character-decomposed DOS (Figure S6(b)) for phase 1. It was confirmed that the computed ionization potential is greater in the distorted phase 1 (6.64 eV) and phase 2 (6.79 eV) than in the planar phase 3 (6.33 eV); these results are commensurate with the magnitude of the band gap (Table 1). This mechanism is also supported by our analysis of the effects of distortion on a single-layered heptazine g-C3N4 nanosheet, where the band gap opening associated with on-site LP-π1 hybridization was observed (Figure S7). This result supports the idea that the interlayer interaction is not the dominant factor for the determination of the band gap. On the other hand, the distortion does not significantly alter the nature of the conduction band minimum (CBM), which is mainly composed of π orbitals of carbon (π1*). The electronic structure of phase 1 is consistent with the result of a previous photoelectron spectroscopy study on tri-s-triazine by Shahbaz et al.55 As described in the previous section, the stability of g-C3N4 can be influenced by the stacking sequence (“micro” and “macro” stacking sequences) and the distortion of the heptazine unit. On the other hand, the electronic structures of g-C3N4 strongly depend on the distortion of the heptazine unit and are not significantly influenced by the stacking order. 3.3. Evolutionary Structure Search of High-Crystallinity Phases under Assumption 2. The XRD data shown in Figure 1b, which will be referred to as the SMS highcrystallinity phase in the following section, has been used as an initial guess for our ab initio evolutionary structure search. However, the composition of the SMS high-crystallinity phase is still unclear as discussed earlier. Figure 6 shows the flowchart of our refinement process for finding consistent crystal structures with an experimentally measured XRD pattern set as the criterion for the evolutionary search. The experimental lattice parameters were used as input guesses, and the evolutionary search based on the adjusted compositions was continued until the criterion was satisfied. Following previous experimental studies, we assumed that C and N are the dominant elements in this highly crystalline phase in the first step, and we introduced potential impurities such as hydrogen, chlorine, or lithium in the subsequent steps until the criterion was satisfied. Through this strategy, we efficiently approached the most reliable structure by gradually increasing the complexity of the system. For the structure search of g-C3N4, we examined the lattice volume of the experimentally determined primitive cell of the SMS sample and found it to be about 1.5 times the cell size of phase 1 (discussed in the last section). In the evolutionary structure search, therefore, we used a larger cell that includes 42 atoms for g-C3N4 (i.e., a cell with the formula C18N24). Interestingly, after sampling more than 3000 structures, a triazine-based g-C3N4 (Figure 7a) was identified as a metastable phase. This new g-C3N4 structure is composed of triazine rings

Figure 6. Flowchart of the evolutionary structure search for highly crystalline phases synthesized through SMS. The lattice parameters (including space group of P63cm) were used only for setting up a series of input crystal structures as initial guesses, and they were generated by random number operators. The initial lattice parameters and the space group were fully relaxed and modified during the evolutionary search by applying genetic operators such as heredity, mutation, etc. Therefore, the obtained structure for each composition possesses a space group that gives the global minimum of the enthalpy of formation in a wide range of crystal symmetries.

instead of heptazine rings, and its total energy is only 0.010 eV higher than that of phase 1 per formula unit. The computed Gibbs free energy of the triazine-based g-C3N4 is about 0.1 kJ/ mol higher than that of the heptazine-based phase 1 at ambient pressure (Figure S3(a)). In addition, the characteristics of this structure are similar to those of the heptazine-based phase 1; the g-C3N4 planes are distorted and a “macro” A−B stacking sequence between the neighboring layers was also observed. However, the calculated phonon dispersion of the triazinebased g-C3N4 shows slightly negative frequencies (Figure S2(c)). The present calculation result reaffirms that the heptazine-based g-C3N4 is the most stable phase, as suggested by the experiments.2,21 However, a recent study56 reported that prospective crystal structures featuring computed dynamically unstable phases should not be fully excluded from the possibility of synthesis. Moreover, the very slight difference between the triazine- and heptazine-based phases reveals that the triazine-based phase could be realized under certain conditions.25 2700


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Figure 7. Predicted structures corresponding to the SMS condition: (a) triazine-based g-C3N4; (b), C3N5H3; (c) C2N3H-P63m; (d) C3N6H3-HCl; (e) C6N9H3-LiCl; (f) C6N9H3-Li3Cl. The small pink and green balls represent H and Li atoms, respectively. The large green balls in (d)−(f) represent Cl atoms. The atoms in the lower layer of the lattices are labeled with yellow crosses.

crystallinity phase synthesized by SMS, the parameters a and b are quite different from the experimental values. The comparison of simulated XRD and experimental patterns

The space group and the lattice parameters of the predicted triazine-based are listed in Table 2, which shows that even though g-C3N4 possesses the same space group as the high2701


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C3N4. Therefore, we calculated the change in Helmholtz free energy for the transition from melam to g-C3N4 in an inert atmosphere using the following equation:

Table 2. Space Groups, Lattice Parameters, And Band Gaps of Predicted Stable Structures Corresponding to SMSa composition g-C3N4 (triazine)

space group P63cm

C3N5H3

P63cm

C2N3H

P63cm P63m

C6N9H3·HCl

Pm

C6N9H3·LiCl

Cmcm

lattice parameters a = b = 8.004 Å

α = β = 90°

c = 6.920 Å a = b = 8.718 c = 6.786 Å a = b = 8.550 c = 6.662 Å a = b = 8.539 c = 6.355 Å a = 8.433 Å b = 8.396 Å c = 6.504 Å a = b = 8.545 c = 6.648 Å

γ = 120° α = β = 90° γ = 120° α = β = 90° γ = 120° α = β = 90° γ = 120° α = β = 90° γ = 119.90°

Å Å Å

Å

α = β = 90° γ = 121.08°

band gap (eV)

C6N11H 9 → 2C3N4 + 3NH3

3.31

(5)

The calculated energy change of the above reaction is about 2.14 eV per formula unit. The very small energy difference between the triazine- and heptazine-based g-C3N4 shows that the SMS of g-C3N4 is thermodynamically unfavorable. The next step is to include H atoms in our structure search. It is not wise to introduce an arbitrary quantity of H atoms, as it will lead to too many compositions and eventually an infinite structure search. As previously mentioned in connection with Figure 2a, the deamination from the precursor to form g-C3N4 is energetically unfavorable in an inert environment. Therefore, it is highly possible that extra ammonia (NH3) exists in the high-crystallinity phase synthesized by the SMS method. The condensation pathways in Figure 2b show that three NH3 groups need to be removed from one melam (C6N11H9) molecule to form g-C3N4. Therefore, in our structure search, we adopted the two compositions of C6N10H6 and C6N9H3, which correspond to the condition of removing one and two NH3 groups from each C6N11H9 molecule, respectively. Since the size of one C6N11H9 molecule is comparable with the area of the (001) plane of the high-crystallinity phase formed by SMS, it is reasonable to assume that there are two C6N10H6 or

4.07 4.47 4.38 3.72

3.38

a

Detailed crystal information on these structures can be found in Crystallographic Information Files of Predicted Structures.

(Figure S8) explicitly proves that they are different structures and refutes the idea that the high-crystallinity phase synthesized by SMS is g-C3N4. Moreover, based on the condensation pathway shown in Figure 2a, we know that melam (C6N11H9) can be regarded as the direct precursor for the triazine-based g-

Figure 8. Comparison of the simulated XRD patterns of (a) C3N5H3, (b) C2N3H (P63cm), (c) C6N9H3·LiCl, and (d) C6N9H3·Li3Cl with the experimental XRD patterns of the highly crystalline samples synthesized by SMS and modified SMS. 2702


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HCl looks similar to that of C2N3H-P63m. The C2N3H layers stack along the same “macro” A−B stacking mode as that of C2N3H-P63m. The side view of C6N9H3·HCl shows that Cl atoms are placed on the same plane as the C2N3H layers. The introduced H atoms are linked with the nitrogen atoms in the triazine rings. Our calculation shows that the band gap gets narrower after the introduction of Cl. However, the value of 3.72 eV (Table 2) is still quite far from the visible spectrum. More importantly, there is still little similarity between the simulated XRD pattern of C6N9H3·HCl and the experimental pattern (Figure S11). Therefore, a new ab initio evolutionary structure search was carried out for the composition of C6N9H3·LiCl (40 atoms/cell), and finally, the most stable configuration with space group of Cmcm (shown in Figure 7e) was obtained. Table 2 shows that the lattice parameters of the relaxed structure of C6N9H3·LiCl are consistent with the experimental data. The simulated XRD pattern of C6N9H3·LiCl (Figure 8c) also shows good consistency with the experimental XRD pattern of the SMS high-crystallinity sample, except for the peak at 18.02°. This inconsistency may be attributed to the different symmetries of the predicted structure (Cmcm) and the experimental one (P63cm). In a previous research, Schnick and co-workers24 found by elemental analysis that the composition of the SMS highly crystalline phase was C12N17.5H6.3Cl1.5Li3.2. To compare with their result, our formula for the predicted structure can be rewritten as C12N18H6Cl2Li2, which shows a lower Li content than the experimentally determined formula. This indicates that extra Li atoms could exist in the lattice cell and might be helpful in stabilizing the P63cm symmetry. As the next step, a series of new structure searches was carried out for the systems with the composition of C6N9H3· Li1+xCl (x = 1, 2, ...). Finally, we arrived at a new structure (Figure 7f) with the composition of C6N9H3·Li3Cl and space group of P63cm; its simulated XRD pattern shows perfect agreement with the experimentally observed XRD pattern (Figure 8d) of the highly crystalline SMS sample. For the first time, we explicitly proved the composition of the highcrystallinity SMS sample and obtained its crystal structure. We noticed that the concentration of Li in the predicted structure of C6N9H3·Li3Cl is twice that of the experimentally determined composition of C12N17.5H6.3Cl1.5Li3.2. This inconsistency comes from the difficulty in precisely determining the composition of a compound with light elements. Figure 7 (panels e and f) shows that the structures of C6N9H3·LiCl and C6N9H3·Li3Cl are quite similar; the voids of the layers of C6N9H3 are stacked upon each other, forming channels along the c axis by “micro” A−B stacking, while the Cl atoms sit at the centers of the void channels and are located on planes that are different from those of the C6N9H3 layers. However, because of the removal of the extra Li atoms, the overlap of the triazine rings in the C6N9H3·LiCl cell (Figure 7e) is not as perfect as that in the C6N9H3·Li3Cl cell (Figure 7f). This deviation can be attributed to the transition from the “micro” A−B stacking to the “macro” A−B stacking, which can stabilize the structure by decreasing the interlayer repulsion and lead to the change in symmetry from P63cm to Cmcm. Since the concentration of Li in C6N9H3·Li3Cl is three times that of Cl, it is not very stable from the point of view of charge compensation. Therefore, we suspected that C6N9H3·Li3Cl might be a metastable phase in comparison with C6N9H3·LiCl. We designed a modified experimental procedure based on the method reported by Bojdys et al.19 to confirm our speculation. In the modified

C6N9H3 molecules per unit cell. Two ab initio evolutionary structure searches were carried out with the compositions of C12N20H12 (44 atoms) and C12N18H6 (36 atoms). Finally, one most-stable structure with the composition of C3N5H3 (the simplest formula) and two most-stable structures with the composition of C2N3H (the simplest formula) were obtained, and they are shown in Figure 7 (panels b and c) and Figure S9, respectively. It is interesting to note that all these structures are layered. Figure 7b shows that the most stable configuration of C3N5H3 is composed of melem (C6N10H6) molecules, and it possesses the space group suggested by the experiment, P63cm, but with larger lattice parameters (Table 2). Two configurations with almost identical energies but with different structural parameters were found for the formula of C2N3H. The one with the space group P63m (Figure 7c) shows a lower energy than the one with the space group P63cm (Figure S9). However, the energy difference is only 0.0002 eV/C2N3H, which is much smaller than the chemical accuracy and can be ignored. Figure 7c shows that the stacking of the neighboring layers in C2N3H-P63m shows a “macro” A−B sequence. As discussed in the previous section, this stacking sequence can fully stabilize the structure and decrease the interlayer distance, which is proved by the values of the parameter c of C2N3H in Table 2. The space group and the lattice parameters of the predicted C3N5H3 and C2N3H-P63cm appear to be very consistent with the experimental data. The simulated diffraction peaks are compared with the experimental XRD patterns in Figure 8 (panels a and b). It is clear that the XRD peak positions of C3N5H3 are shifted toward lower angles when compared to the experimental peaks, whereas the XRD peak positions of C2N3H-P63cm are very consistent with the experimental data. Furthermore, the relative intensities of the peaks of both C3N5H3 and C2N3H-P63cm are quite different from those obtained in the experimental XRD data. The band structures of all the predicted structures (Figure S10) were calculated, and they showed that the band gaps of C3N5H3, C2N3H-P63m, and C2N3H-P63cm are in the range from 4.07 to 4.47 eV (Table 2), which are far beyond the visible spectrum (1.65−3.27 eV). Previous investigations1−4 have shown the visible-light-activated photocatalysis property of the SMS highcrystallinity materials. Therefore, it appears that our structure search within the composition of C−N−H has yet to reach the right structure. Before introducing new elements to the C−N−H system, we needed to determine the best composition for the starting point for further structure searches. Table 2 shows that the lattice parameters of C3N5H3 are larger than those extracted from the experimental data, while those of C2N3H are smaller. We expect that the introduction of other species will further expand the lattice volume but also cause further deviation of the structure from the experimental results if C3N5H3 is adopted as the initial composition. Thus, we chose the composition of C2N3H as the starting composition for the subsequent evolutionary structure search. First, we introduced Cl atoms into the C2N3H-P63m unit cell by adding one Cl atom per C2N3H layer. Meanwhile, the same number of H atoms was also added for charge compensation; in other words, C6N9H3·HCl (40 atoms/cell) was adopted as a search composition for the C−N−H−Cl system. From the ab initio evolutionary structure search, a structure with space group of Pm was found to be the most stable configuration of C6N9H3·HCl (Figure 7d). The predicted structure of C6N9H3· 2703


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Figure 9. Proposed reaction pathway to synthesize highly crystalline g-C3N4 starting from C6N9H3·LiCl.

procedure, we boiled our final sample for 5 min instead of just washing it with boiling water. The sample was then centrifuged it at 16000 rpm for 10 min. This procedure was repeated at least 15 times. We present the XRD pattern of this modified SMS sample in Figure 8c together with those of the SMS highcrystallinity phase and the predicted C6N9H3·LiCl result. It clearly shows that a new peak appears at about 18°, which is consistent with the XRD pattern of the predicted C6N9H3·LiCl structure. The appearance of this new peak indicates the transition of the symmetry from P63cm to Cmcm and validates our hypothesis. Therefore, we claim that a more stable new phase of C6N9H3·LiCl has been discovered theoretically and validated experimentally for the first time. The computed band structure of C6N9H3·LiCl presents a direct band gap of 3.38 eV, which is quite close to the experimental value of 3.07 eV (Figure S12). Moreover, both the top of the valence band and the bottom of the conduction band are very flat (Figure S11(a)), indicating the good photoabsorption ability of C6N9H3·LiCl as a photofunctional material.57 This clearly supports the good photocatalytic performance of this material1−9 even in the presence of a fairly wide band gap. Through a series of high-throughput ab initio evolutionary structure searches, we confirmed that the high-crystallinity SMS phase is not g-C3N4; instead, the predicted structure should be C6N9H3·Li3Cl. More importantly, we proved that the C6N9H3· Li3Cl is a metastable phase, and we discovered the more stable structure with a composition of C6N9H3·LiCl theoretically and then validated our prediction by a modified experimental procedure. The study so far explicitly shows the power of the state-of-the-art high-throughput structure search method for the prediction of structures of novel materials. One question that has been raised is the following: Can we give further clues on how to synthesize new materials like highly crystalline gC3N4? Our answer is definitely “Yes”.

The space group of the predicted triazine-based g-C3N4 is P63cm, which is the same as the symmetry of C6N9H3·Li3Cl and also quite similar to that of C6N9H3·LiCl. Therefore, the stable structure of C6N9H3·LiCl can be a good starting point to synthesize highly crystalline g-C3N4 by the postsynthesis modification (PSM) method, which has been highlighted in recent studies.58,59 These two structures of C6N9H3·HCl and C6N9H3 (C2N3H) can be regarded as the intermediates for the transition from C6N9H3·LiCl to g-C3N4. Consequently, a possible reaction pathway to produce highly crystalline gC3N4 from C6N9H3·LiCl has been proposed, as shown in Figure 9. The possible experimental procedure is described in detail as follows. The first step is to remove Li from C6N9H3·LiCl or, more precisely, to replace Li with H. Our experiments on the removal of Li from C6N9H3·Li3Cl have proved that the lithium ion can be easily removed because of its small size (about 0.76 Å). However, the structure of C6N9H3·LiCl is indeed very stable and the charge compensation has already been achieved. The Li ions cannot be removed by further boiling and centrifuging. Hence, we suggest dispersing C6N9H3·LiCl in an aqueous HCl solution to replace Li+ with H+. The high densities of Li+ and H+ in C6N9H3·LiCl and in the HCl solution, respectively, will drive the ion exchange between Li+ and H+. The removal of Cl ions in the second step could be slightly more difficult because of their larger size, about 1.81 Å. Two possible solutions are suggested. The first solution is to peel the bulk C6N9H3·HCl into nanosheets by soft chemistry synthesis; the Cl ions can then be easily removed by a chemical method to obtain C2N3H nanosheets. Through the oxidation of the C2N3H nanosheets, graphitic carbon nitride can be synthesized. Another option is to heat C6N9H3·HCl in a gas flow that contains H2 at a medium to high temperature. The small H2 molecules can diffuse into the C6N9H3·HCl to drag the Cl out in the form of HCl. The continuous gas flow can remove the HCl from the sample surface to perpetuate the reaction. However, the 2704


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Chemistry of Materials concentration of H2 and the operating temperature should be carefully controlled to protect the sample from possible hydrogen etching. Finally, highly crystalline g-C3N4 can be obtained by heat-treating C2N3H in an oxidizing environment. Recently, Bojdys and co-workers25 detected triazine-based gC3N4 during SMS of poly(triazine imide) with intercalated bromide ions (PTI/Br) at the gas−liquid and solid−liquid interfaces in the reactor. Since the halogens can be easily removed at the interface, this result supports the feasibility of the last step of the proposed procedure of g-C3N4 shown in Figure 9. Therefore, the removal of halogens would be the key step in the synthesis of high-crystallinity g-C3N4 by SMS.

4. CONCLUSION A series of high-throughput ab initio evolutionary structure searches were carried out to predict the structures of g-C3N4 and related compounds corresponding to two different synthesis methods: thermal polycondensation in an oxidizing environment and SMS in an inert environment. For the synthesis via thermal polycondensation, the structures for the most stable heptazine-based g-C3N4 and the robust metastable phases, phases 1, 2, and 3, were predicted. Our search results revealed that unlike other planar layered structures, the stable configurations of g-C3N4 are distorted. On the basis of the results of structure prediction and transition state searches, we demonstrated that the phase transition from phase 2 to phase 1 is a new mechanism to explain the temperature dependence of the band gap of g-C3N4. A complete and renewed understanding of the relationship between the electronic structure and the crystal configurations of g-C3N4 has been presented based on the newly discovered structures of g-C3N4. A model was developed to explain the influence of the distortion of the heptazine unit on the electronic structure of g-C3N4. For the SMS process, we predicted a series of structures with different compositions of C3N4, C3N5H, C2N3H, C6N9H3·HCl, C6N9H3·Li3Cl, and C6N9H3·LiCl through extensive highthroughput ab initio evolutionary structure searches. We clarified that the controversial structure of the previously reported high-crystallinity SMS phase was C6N9H3·Li3Cl instead of g-C3N4. Furthermore, we revealed that C6N9H3· LiCl is a more stable high-crystallinity phase than C6N9H3· Li3Cl. By combining the theoretical structure search with improved SMS experiments, the structure of C6N9H3·LiCl has been validated for the first time. On the basis of the predicted stable structures, a very promising reaction pathway to synthesize highly crystalline g-C3N4 from C6N9H3·LiCl has been proposed.

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heptazine-based Phase 1 and Phase 2; (Figure S5) electronic structure of Phase 2; (Figure S6) electronic structures of distorted Phase 1 and planar Phase 3; (Figure S7) electronic structures of distorted and planer g-C3N4 single layers; (Figure S8) simulated XRD pattern and calculated band structure of triazine-based g-C3N4; (Figure S9) predicted structure of C2N3H-P63 cm; (Figure S10) band structures for C2N3H-P63 cm, C2N3H-P63m, and C3N5H3; (Figure S11) comparison of simulated XRD pattern of predicted C6N9H3·HCl with that of the highly crystalline SMS sample; (Figure S12) band structure and UV/vis absorption spectrum of C6N9H3·LiCl; (Table S1) structure details of heptazinebased g-C3N4 configurations; (Table S2) structure and ionization potentials of the three most stable heptazinebased g-C3N4 configurations; typical USPEX input file for the prediction of triazine-based g-C3N4; crystallographic Information Files of predicted structures (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] *E-mail: [email protected] ORCID

Junjie Wang: 0000-0002-6428-2233 Jinhua Ye: 0000-0002-8105-8903 Naoto Umezawa: 0000-0001-9572-9790 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.W. is an International Research Fellow of the Japan Society for the Promotion of Science (JSPS). We acknowledge the financial support from JSPS through project P14207. This work is partly supported by the World Premier International Research Center Initiative on Materials Nanoarchitectonics (MANA), MEXT, and by the Core Research for Evolutional Science and Technology (CREST) program and Materials research by Information Integration Initiative (MI2I) project of the Japan Science and Technology Agency (JST). J.W. thanks Dr. Nguyen Thanh Cuong of NIMS, Prof. Tomofumi Tada and Prof. Hirofumi Akamatsu of Titech and Prof. Daniel Fredrickson of UW-Madison for useful discussions and suggestions. N.U. thanks Dr. Christian Joachim and Dr. Masakazu Aono of NIMS for their useful advice.

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ASSOCIATED CONTENT

REFERENCES

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b02969. Details of the computational and experimental methods; (Figure S1) test results of different exchange-correlation functionals; (Figure S2) computed phonon dispersions of heptazine-based Phase 1 and Phase 2 and triazinebased g-C3N4; (Figure S3) computed Gibbs free energy and equations of states of heptazine-based Phase 1 and Phase 2 and triazine-based g-C3 N4; (Figure S4) calculation results for the phase transition between 2705


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Determination of Crystal Structure of Graphitic Carbon Nitride: Ab Initio

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